Deposito Algebra Lineal 41

Remove["Global`*"] u = {1, m, -2}; v = {m + 1, 0, 1}; w = {2, 0, 2 m - 1}; Reduce[a*u + b*v + c*w == {0, 0, 0}] (m == 0 && b == -c && a == -c) || (m == \frac{-3}{2} || m == 1) && b == c - 2 c m && a == 0) || (-3 + m + 2 m^2 + 6 b == 0 && c == 0 && b == 0) Solve[-3 + m + 2 m^2 == 0, m] {m -> \frac{-3}{2}, m -> 1} mat = Transpose[{u, v, w}]; MatrixForm[mat] \begin{pmatrix} 1 & 1 + m & 2 \\ m & 0 & 0 \\ -2 & 1 & -1 + 2 m \end{pmatrix} Solve[Det[mat] == 0] {m -> \frac{-3}{2}, m -> 0}, {m -> 1} u = u /. m -> 1; v = v /. m -> 1; w = w /. m -> 1; sol = Solve[a*u + b*v + c*w == {-2, 2, 2}] {{a -> -2, b -> -2, c -> 0}} xp = {a, b, c} /. sol[[1]] {-2, -2, 0} Remove["Global`*"] v1 = {1, 0, 1}; v2 = {-2, 0, -1}; v3 = {2, -1, 1}; u1 = {0, 1, -1}; u2 = {1, 0, 1}; vc = 3*v1 - 2*v2 - v3 {5, 1, 4} ecuaciones = a*u1 + b*u2 {b, a, -a + b} Solve[vc == ecuaciones] {{a -> 1, b -> 5}} sol = Solve[a*u1 + b*u2 == vc] {{a -> 1, b -> 5}} vb = {a, b} /. sol[[1]] {1, 5} Remove["Global`*"]